On the minimum orbital intersection distance computation: a new effective method

Hedo, J. M.; Ruiz, Manuel Pérez; Peláez, Jesús

doi:10.1093/mnras/sty1598

Cited by 13 publications

(21 citation statements)

References 11 publications

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“…We conclude that our algorithm looks quite competitive and probably even outperforming the benchmarks obtained by Hedo et al (2018) for their set of tested algorithms (60-80 µs per orbit pair on a Supermicro/Xeon hardware). They used double precision rather than long double one.…”

Section: Practical Validation and Performance Benchmarksmentioning

confidence: 61%

“…Email address: r.baluev@spbu.ru (Roman V. Baluev) This problem is investigated over decades already, see e.g. (Sitarski, 1968;Dybczyński et al, 1986) and more recent works by Armellin et al (2010); Hedo et al (2018).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Hedo et al (2018) suggested a method that does not rely on necessary determination of all the stationary points for the distance. It basically splits the problem in two tasks of 1D optimization, so this method belongs to the 1D class.…”

Section: Introductionmentioning

confidence: 99%

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Fast error-controlling MOID computation for confocal elliptic orbits

Baluev

Mikryukov

2019

Astronomy and Computing

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We present an algorithm to compute the minimum orbital intersection distance (MOID), or global minimum of the distance between the points lying on two Keplerian ellipses. This is achieved by finding all stationary points of the distance function, based on solving an algebraic polynomial equation of 16th degree. The algorithm tracks numerical errors appearing on the way, and treats carefully nearly degenerate cases, including practical cases with almost circular and almost coplanar orbits. Benchmarks confirm its high numeric reliability and accuracy, and that regardless of its error-controlling overheads, this algorithm pretends to be one of the fastest MOID computation methods available to date, so it may be useful in processing large catalogs.

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Section: Practical Validation and Performance Benchmarksmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

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Fast error-controlling MOID computation for confocal elliptic orbits

Baluev

Mikryukov

2019

Astronomy and Computing

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“…However if ρ(E, E ′ ) is computed by the same software, the dimensionless quantity t MOID /t EST should keep approximately the same value. When other software is used (see for example, Gronchi, 2005;Hedo et al, 2018), the value of t MOID /t EST may differ significantly from our one. Indeed, benchmarking tests carried out in our previous article (Baluev and Mikryukov, 2019) reveal that computational performance (time of calculating ρ(E, E ′ ) per one pair) vary considerably from one software to another (see also Hedo et al, 2018).…”

Section: The Lower Bound Of the Distance Between Orbitsmentioning

confidence: 86%

“…From a practical point of view, the main difficulty of the MOID computation appears due to the lack of the general analytical solution expressing the result via explicit functions of osculating elements. A need of numerical methods arises therefore (Gronchi, 2005;Hedo et al, 2018;Baluev and Mikryukov, 2019).…”

mentioning

confidence: 99%

A lower bound of the distance between two elliptic orbits

Mikryukov

Baluev

2019

Celest Mech Dyn Astr

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We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is expressed explicitly, using only elementary functions of orbital elements, and allows us to significantly increase the speed of processing for large asteroid catalogs. Benchmarks confirm high practical benefits of the lower bound constructed.

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Revisiting the computation of the critical points of the Keplerian distance

Gronchi,

Baù,

Grassi

2023

Celest Mech Dyn Astron

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We consider the Keplerian distance d in the case of two elliptic orbits, i.e., the distance between one point on the first ellipse and one point on the second one, assuming they have a common focus. The absolute minimum $$d_{\textrm{min}}$$ d min of this function, called MOID or orbit distance in the literature, is relevant to detect possible impacts between two objects following approximately these elliptic trajectories. We revisit and compare two different approaches to compute the critical points of $$d^2$$ d 2 , where we squared the distance d to include crossing points among the critical ones. One approach uses trigonometric polynomials, and the other uses ordinary polynomials. A new way to test the reliability of the computation of $$d_{\textrm{min}}$$ d min is introduced, based on optimal estimates that can be found in the literature. The planar case is also discussed: in this case, we present an estimate for the maximal number of critical points of $$d^2$$ d 2 , together with a conjecture supported by numerical tests.

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On the minimum orbital intersection distance computation: a new effective method

Cited by 13 publications

References 11 publications

Fast error-controlling MOID computation for confocal elliptic orbits

Fast error-controlling MOID computation for confocal elliptic orbits

A lower bound of the distance between two elliptic orbits

Revisiting the computation of the critical points of the Keplerian distance

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